Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
732 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23765074 | C2 | semidirect |
| 3. #23763920 | C2 | semidirect |
| 8. #19099313 | C4 | semidirect |
| 10. #19099293 | C4 | semidirect |
| 198. C79 | #12779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777814 | 2 |
| #23765074 | 2 |
| #23763920 | 2 |
| #23763784 | 2 |
| C79×#2126 | 2 |
| #12779 | 79 |